Question

when we want to find the equation of the locus moving point in the from the given point, what formula should we use? this is coordinate geometry topic.

Answer 1

@jtvatsim can you help me?

Answer 2

hmm... I'm not too familiar with the equation of the locus.

Answer 3

looks like the equation will be some sort of parabola based on what I'm reading.

Answer 4

I've found something online that seems to make sense. I'll post it below.

Answer 5

great

Answer 6

This is based off of a quote from math.stackexchange:

Let (x,y) be the unknown point. It's distance from the y axis is given by |x|. It's distance from the given point (a,b) is given by \[\sqrt{(x-a)^2 + (y-b)^2}\]
Since we want both distances to be equal we must have: \[|x| = \sqrt{(x-a)^2 + (y-b)^2}\]
In other words, if we get rid of the square root by squaring: \[x^2 = (x-a)^2 + (y-b)^2\]

Answer 7

I imagine that the above could be simplified given actual numbers. For instance, take (1, 2) as the given point, then the equation is \[x^2 = (x-1)^2 + (y-2)^2\] which becomes \[x^2 = x^2 - 2x + 1 + y^2 - 4y + 4\] or you can write \[x = \frac{1}{2}(y^2 -4y + 5)\]

Answer 8

so, if the question says: find the equation of the locus of the moving point P (x,y) such that it is equidistant to the points C and D.

I must use the formula

PC = PD
\[ \sqrt{(x-x) + (y-y)} = \sqrt{(x-x) + (y-y)}\]

Answer 9

?? is it like this?

Answer 10

I think we have to use different notation, let me think for a moment. You are on the right track though. :)

Answer 11

ok ok.

Answer 12

Actually, I feel like that is a different type of question. I'm basically thinking of it this way:

Answer 13

But we need the point to be equidistant from C and D so certainly it has to look like this